Simulation Study of Shearing Effects on Carbon Nanotube/Polymer

Simulation Study of Shearing Effects on Carbon Nanotube/Polymer

Ali Erdem Eken (Autor)
Simulation Study of Shearing Effects on Carbon
Nanotube/Polymer Composites
https://cuvillier.de/de/shop/publications/6162
Copyright:
Cuvillier Verlag, Inhaberin Annette Jentzsch-Cuvillier, Nonnenstieg 8, 37075 Göttingen, Germany
Telefon: +49 (0)551 54724-0, E-Mail: [email protected], Website: https://cuvillier.de
Introduction
1 Introduction
Nowadays polymer matrix nanocomposites are widely used in industrial applications because
of their exceptional properties that can be tailored to specific requirements. Incorporating
nanoparticles into the polymer matrices to improve the electrical (1-4), thermal (5-9) and
mechanical (5, 7, 10-15) properties of the polymers have been readily investigated. The
insulating nature of polymers is desirable for many applications. However in the fields such
as oil, mine and chemical facilities, static charging can be dangerous. On the insulating
polymer surface, static charge can induce fire or even cause explosion. Furthermore, in the
electronic industry, the need of conductive or anti-static polymeric materials is growing
everyday (16). In some aerospace components materials with improved conductivity should
be used to achieve electrostatic discharge and electromagnetic-radio frequency interference
protection. The use of carbon black with high filler loadings seems to be a solution for this
problem. Using high volume fractions increases the cost and the weight of the final product
and also degrades the mechanical properties of the composite and reduces the smoothness of
the surface finish. Increasing filler volume fraction also increases the viscosity of the melt,
which is critical in thin wall molding applications (17).
Carbon nanotubes (CNTs) are novel materials that have promising properties and can replace
carbon blacks. Multiwalled carbon nanotubes (MWCNTs) are cheaper and thus they are
preferred over single walled carbon nanotubes (SWCNTs) in industrial applications (17).
Previous studies showed that using multiwalled carbon nanotubes in place of carbon black
promotes to a lower percolation threshold and higher conductivity in bulk samples (18).
Percolation threshold is defined as the critical concentration where the transition from an
insulating to a conductive system occurs. Percolation is previously described by many
statistical theories (19) which assumes random distribution of the conductive fillers but in
reality these theories predict percolation thresholds orders of magnitude larger than found in
experimental studies. Moreover percolation threshold differs greatly among the studies
because these studies do not possibly consider the particle movement during the
manufacturing steps. Particles can move via shear forces or electrical fields during processing
which leads to very percolation thresholds (20). Achieving low percolation threshold is of
industrial interest because it reduces the weight and the production cost by decreasing the
filler concentration that is necessary to achieve the desired conductivity level.
1
Introduction
During processing of these composites, materials are exposed to significant deformation that
changes the microstructure and affects the properties of the final products. One of the main
reasons of not having many commercial CNT/polymer composite products in the market is
the difficulty to control the processing conditions and obtaining reproducible properties with
carbon nanotubes. An agglomerated or dispersed microstructure could be achieved by
changing the processing parameters. Initial dispersion of the nanotubes within the polymer
matrix is crucial to improve the mechanical properties because remaining agglomerates could
behave as defects (21). Although an agglomerated-network structure is not preferential for the
mechanical properties, it is beneficial for the electrical conductivity in these composites.
Therefore, in order to improve the material properties and manufacturing process, a clear
understanding of how these materials react to the flow fields is required.
The purpose of this work is to understand the dependence of the electrical properties on the
processing variables and material properties of CNT/polymer composites. While previous
simulation studies have illustrated that fiber shape influences the electrical properties of CNT
composites, they did not consider the effects of nanotube shape, composite microstructure and
imposed shear flow together on the electrical properties of these composites. In this study, we
employ fiber-level simulation method developed by Switzer and Klingenberg (22) to examine
the effects of both material properties and imposed flow on the microstructure and electrical
conductivity of CNT/polymer composites. The electrical conductivities of the composites are
calculated using a resistor network algorithm developed by Tozzi (23). We show that fiber
shape, aspect ratio, shear history and interparticle interactions influence the formation and
dispersion of agglomerates in shear flow and determine the structure and conductivity of the
composites. In order to explain the extremely low percolation thresholds obtained by applying
moderate shear rates, simulation studies are crucial. Besides single carbon nanotubes cannot
be observed during processing with commercial characterization methods. Therefore
simulations are the only way to get insight the movement of the carbon nanotubes in polymer
melts which determines the microstructures and properties of the final composites. In
addition, simulations have the great advantage to work on the effects of each parameter
separately. Throughout this study we give the results of previously performed experimental
studies on the microstructure and electrical conductivity of CNT/polymer composites and we
show that our model could closely reproduce the dynamics of composite microstructure
formation and electrical conductivity behavior of these composites. Also we observe many
new phenomena which would help us to understand and benefit more from these systems.
2
Introduction
After this introduction, Chapter 2 provides the literature review which gives the necessary
scientific background and literatures for understanding the properties of carbon nanotubes and
CNT/polymer composites where we mainly focus on the electrical properties. Chapter 2
includes the percolation theory that concerns with the transport in inhomogeneous conductors
which exhibits percolation threshold. The initial attempts to find out the relationship between
the electrical percolation threshold and the excluded volume of the particles are also
explained. Insulator to conductor transition in CNT/polymer composites was previously
explained by these theories. A brief discussion on the electrical conduction mechanisms such
as tunneling in CNT/polymer composites is given to provide a better understanding to these
materials.
To estimate the final properties and microstructure of the composites after manufacturing
process, understanding the fiber dynamics in suspensions is important. The previous attempts
to describe the behaviors of fibers under flow fields are given in Chapter 3. Fiber-level
simulation technique that is known to reproduce observed fiber suspension behavior under
flow fields is also described in this chapter. This technique includes fiber flexibility and interfiber interactions such as friction and attractive/repulsive forces which makes simulations
realistic. Using these simulations can help us to predict the formation and destruction of the
aggregates under shear flow and henceforth help to understand the response of these materials
to the processing conditions. The Monte Carlo method which was previously developed by
Tozzi (23), used to generate randomly oriented well dispersed nanotube suspensions is also
described in Chapter 3. By using this method, simulation results are compared with
theoretical predictions of electrical conductivity and percolation thresholds to validate the
simulations. Chapter 4 describes the resistor network algorithm which employs periodic
boundary conditions and is used to predict electrical conductivity and percolation thresholds
of sheared and randomly oriented CNT/polymer composites.
In Chapter 5, we investigate the combined effects of carbon nanotube properties such as
aspect ratio, curvature, anisotropy and tunneling length on the electrical conductivities of
CNT/polymer composites. We show that results for percolation thresholds in static systems
agree with predictions and experimental measurements. In agreement with previous research
we also find that lower percolation thresholds are obtained for less curved and high aspect
ratio nanotubes. Increasing tunneling distance between the conductive fillers decreases the
3
Introduction
electrical percolation threshold of the composites. When the anisotropy of the system
increases, the conductive network is formed at higher filler concentrations.
We investigate the effects of both material properties and imposed shear flow on the electrical
percolation threshold of CNT/polymer composites in Chapter 6. We show that nanotube
properties determine the final microstructure hence final properties of the composites.
Percolation threshold in sheared suspensions are observed at lower volume fractions than both
non-sheared suspensions and theoretical predictions. The effect of nanotube shape is found to
be different for sheared and non-sheared suspensions. For sheared suspensions, increasing
nanotube curvature resulted in a decrease in percolation threshold because of the
agglomeration dynamics. Our prediction is that increasing nanotube curvature favors the
formation of agglomerates in sheared suspensions which leads to formation of percolative
networks.
The rate of imposed shear flow on microstructure and electrical conductivity is analyzed in
Chapter 7. We also discuss the effect of agglomeration on electrical conductivity. Applying
high shear rates cause de-agglomeration and alignment of the nanotubes in the flow direction
with a decrease in composite conductivity. We show that upon shearing at constant shear rate,
the system attains a state with substantially constant electrical conductivity, nanotube
orientation and agglomerate size that are a function of the applied shear rate. The state
reached for a given shear rate is independent of the initial state of orientation and
agglomeration.
Finally, a brief review which gives general discussion on the study and summary of the key
conclusions as well as recommendations for future work is given in Chapter 8.
These simulations give us insight about the structural and electrical conductivity changes
during production processes, henceforth helping us to understand production processes and
their effects on product properties. It has been experimentally demonstrated that under some
conditions, ultra low percolation thresholds have been obtained (2) which are not properly
described by models that do not account for flow. Such class of models therefore, cannot be
used to design or control a large scale process, where a failed batch or production run would
have a large cost in time and materials. For such applications, improved models are needed,
that quantitatively describe the relation between conductivity and flow processing parameters.
4
Carbon Nanotubes
2 Literature Survey
2.1 Carbon Nanotubes
Carbon nanotubes are produced by the catalyzing effect on the gaseous species from the
thermal decomposition of hydrocarbons (24). In 1991, Iijima (25) imaged multiwalled carbon
nanotubes using a transmission electron microscopy (TEM). This is the first experimental
evidence of the existence of the carbon nanotubes (Figure 2.1). After this work CNT research
has been expanded at an extreme speed.
Carbon nanotubes are rolled graphene sheets into cylinders to form tubes and the way the
sheet is rolled determines the physical properties of the nanotube. The nanotubes can be tens
of millimeters long but with small diameters as low as
(26).
Figure 2.1. TEM observation of multiwalled nanotubes first reported by Iijima (25).
Tube walls are made up of a hexagonal lattice of carbon atoms and they are capped at their
ends by a fullerene-like molecule (27). Nanotube structure can be specified by its chiral
vector,
and chiral angle,
based on the orientation of the tube axis with respect to the
hexagonal lattice (Figure 2.2). The chiral vector can be described by;
5
Literature Survey
(2.1)
where
and
are integers,
and
are the two basis vectors of graphite with
(2.2)
and
(2.3)
where
and chiral angle is defined as;
(2.4)
Figure 2.2. A hexagonal graphite sheet is rolled to form a carbon nanotube (28).
6
Carbon Nanotubes
The arrangement of the carbon atoms changes the electronic structure of the carbon
nanotubes. The chiral angle separate carbon nanotubes into three different classes by their
electronic properties; armchair (
(
,
,
), zigzag (
,
,
) and chiral
). Armchair carbon nanotubes are metallic and zig-zag and chiral
nanotubes can be semi-metallic or semiconductors (29). Rolling a sheet of graphene to obtain
three different carbon nanotube types is given in Figure 2.3.
Parameters such as the carbon nanotube diameter are related to chiral vector and can be
determined from
and
;
(2.5)
where
where for graphite C-C bond length is
and for
it is
(24).
Figure 2.3. Rolling a sheet of graphene to obtain three different carbon nanotube types.
Structure of a multiwalled carbon nanotube (27).
7
Literature Survey
There are mainly two types of carbon nanotubes, so called “single-walled carbon nanotubes
(SWCNT)” and “multi-walled carbon nanotubes (MWCNT)”. SWCNTs are hollow single
cylinders of a graphene sheet which are defined by their diameter and chirality. SWCNTs can
be either metallic or semiconductive (30). MWCNTs posses two or more concentric single
wall tubes with diameters ranges from
up to
. By using electron and x-ray
diffraction studies, Saito et al. (31) measured the mean value of the interlayer spacing
between the graphitic sheets in nanotubes as
. The graphitic shells are held together
by secondary van der Waals forces.
Carbon nanotubes exhibit a large surface atom to bulk atom ratio. Percentage of surface atoms
decreases with increasing number of shells (100% for SWCNTs). Therefore the theoretical
specific surface area (SSA) of the SWCNTs is very high up to
(32). This value
mostly depends on the wall number of MWCNTs (for a MWCNT 35 nm in diameter with 40
walls, Peigney et al. (32) calculated the SSA as
). This high SSA of the carbon
nanotubes is one of the main reasons for the high tendency to agglomerate in a liquid media
(33).
High aspect ratio (300-1000) of the nanotubes is a very important characteristic because of its
use as nanoscale fillers to produce composite materials with improved properties (34).
Because of their excellent mechanical, electrical and thermal properties, they are considered
as fillers for advanced applications. Both SWCNTs and MWCNTs show unique properties
and can be used in composite materials.
2.2 Properties of Carbon Nanotubes
Carbon nanotubes exhibit extremely high elastic modulus (
) which is 10-100 times
stronger than steel and comparable to diamond (35). They have also superior thermal and
electrical properties. Their electrical conductivities are
stable up to
and can be as high as
and they are thermally
in vacuum and their thermal conductivity is greater than diamond (28)
(34).
The comparison between the theoretical properties of carbon nanotubes and some commercial
high-performance fibers are listed in Table 2.1 (36);
8
Properties of Carbon Nanotubes
Table 2.1. Typical properties of CNT, Carbon fiber, Spectra and Kevlar 49 (36, 37).
Tensile Strength
(GPa)
Tensile
Modulus (GPa)
Density (g/cm3)
Carbon Nanotube
Carbon
(MWCNT)
Fiber
11-63 GPa
4-7
3.1
3.6-4.1
0.9-1.9 TPa
150-950
105
130
1.4
1.7-2.2
0.97
1.44
~106
500 (38)
Spectra®
Kevlar
49®
Electrical
Conductivity
(S/m)
More detail regarding electrical properties of carbon nanotubes is given below.
Electrical transport through the SWCNTs has been extensively studied in the past years and
many applications based on their exceptional electronic properties have been proposed for the
future’s nanoscale devices. The transport properties of carbon nanotubes depend on the
electronic band structure which is composed of 1-dimensional (1D) subbands (26). By rolling
the graphene sheet, electronic wave functions are modified giving a rise to the 1D subbands
(24). SWCNTs are nearly perfect systems for 1D conductors. When compared with other 1D
conductors, SWCNTs exhibit several advantages such as being atomically uniform and well
defined as well as having large spacing between their 1D subbands showing that the 1D
nature is conserved even at the room temperature and above. Also, compared to the molecular
wires, SWCNTs exhibit a robust and chemically inert structure (39).
SWCNTs can be classified into 3 classes according to their bandgaps:
SWCNTs with small band gap are partially conducting (
). These type
of nanotubes exhibit a strong dependence on the temperature (33).
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Literature Survey
Metallic SWCNTs with
. These types of nanotubes are rare because of the
perturbations existing in all SWCNTs which increase the band gap (40). However they
do not show a Peierls instability like the other 1D materials. Even at low temperatures
they do not undergo a metal-to-insulator transition (41). Reduced electron scattering
provide metallic SWCNTs a high current density (
) up to 3 orders of
magnitude higher than copper (24).
(40). The band gap is inversely
Semiconducting SWCNTs with
proportional to the tube diameter (24). When gate voltage is zero, current can pass
through carbon nanotubes and conductance is by unoccupied valence states.
Increasing the gate voltage changes the conductor type from p-type to n-type (42).
Since there is a confinement effect on the tube circumferences, MWCNTs behave like
quantum wires. They are composed of many SWCNT shells having different band gaps
provides their metallic nature (30). Also, nanotubes are ballistic conductors because their
resistances depend on the number of available conduction channels and the transmission
contacts. Electrons can travel along the nanotube without any scattering because scales are
normally smaller than the scattering lengths (43). In ballistic transport, electrons do not
experience any scattering or resistance. Hence, no energy is dissipated along the nanotube and
large currents can be conducted without energy loss. Therefore the expected quantized
conductance of a metallic nanotube is
(40).
For the semiconducting nanotubes, conduction is diffusive and after neglecting the coherence
effects, resistance of a tube can be written as;
(2.6)
where
is the tube length, is the electron mean-free path and
(40).
The environmental effects or even disordered structure of the carbon nanotubes can influence
the electronic and optical properties of the tubes (24, 33). Localized defects in the lattices,
fluctuations in electrostatic potential and mechanical deformations can modify the band gap
of the nanotubes (40). Applying mechanical stretching (42, 44), axial magnetic field (42),
10
Polymer Based CNT-Filled Materials
internal defects such as atomic vacancies (45, 46), impurities (47-52) or even agglomeration
(24) were proved to change the band structure of the nanotubes. Branden et al. (53) showed
the effect of silicon impurities on the electronic properties of carbon nanotubes by reporting
density functional theory calculations. Added Si atoms opened the band gap of metallic
carbon nanotubes ranging between
to
. In their study Cartoxia et al. (54)
determined that BN-pair addition turned the metallic tubes to semiconducting. It is not easy to
generalize the effects of disorder because of the coexistence of the disorder sources and
variability of the nanotube properties. Detailed information can be found in (40).
Some potential applications of carbon nanotubes are: vacuum microelectronics, hydrogen
storage, nanoprobes and sensors, templates and electron emission devices such as cathode-ray
lighting elements, flat panel display and gas-discharge tubes (55).
2.3 Polymer Based CNT-Filled Materials
Carbon nanotubes are considered as ultimate reinforcing materials due to their superior
electrical, mechanical and thermal properties. Carbon nanotubes are widely used to reinforce
polymer (4, 56-59), ceramic (58, 60-65) and metal (66-69) matrices.
As discussed in (36) some previously reported polymer matrices for carbon nanotube fillers
are; semicrystalline (70, 71) and amorphous (72, 73) thermoplastics, thermosetting (2, 18, 74)
resins, water soluble polymer (75), liquid crystalline polymer (76) and conjugated polymers
(77, 78). Carbon nanotubes were previously used to improve the polymeric materials’
properties such as tensile modulus (79, 80), tensile strength (81), torsional modulus (82),
compressive strength (83), fatigue behavior (84), toughness (83), glass transition temperature
(85, 86), electrical conductivity (1, 2), thermal conductivity (5, 6), solvent resistance (87) and
optical properties (88, 89).
Polymers are widely used in numerous fields because of their advantages over other materials
such as lightness, low-cost, chemical resistance and easy processing (30). Carbon nanotubes
has found many applications in military (90) and space (91). In military applications, carbon
nanotube composites can be used as structural composites/adhesives, coatings and smart
materials. Reducing the total weight of component by manufacturing one-piece sections from
11
Literature Survey
composites and incorporating health monitoring-systems (92, 93) can be stated as the greatest
opportunities for military and aerospace applications. Besides, carbon nanotube composites
have also been used as coatings for radar absorption or radar transparency. Biosensors,
thermal protection via ablation and protective military uniforms are other potential
applications of carbon nanotube composites (90).
Incorporating carbon nanotubes into polymers increases the electrical conductivity of the
materials while leaving other properties and behaviors unaffected (24). They can transform an
insulating matrix to a conductive composite at very low volume fractions because of their
high aspect ratio (3). Electrostatic discharge (preventing fire or explosion hazards in
combustible environments or perturbations in electronics), electrostatic painting (preventing
charged paint droplets from being repelled) and electromagnetic interference shielding are the
main interesting areas regarding the electrical conductivity (24).
Polymeric coatings with sufficient electrical conductivity to discharge the electricity are
needed for space structures. Energetic particles can penetrate inside the surface layers causing
an electrostatic charging in the insulating materials on a space structure. Hence discharging is
crucial to prevent the fatal damage on the electronic parts (91). Required surface conductivity
to provide the electrostatic discharge is
Figure
2.4
shows
the
experimental
(94).
results
of
electrical
conductivity
of
the
SWCNT/Polystyrene composites as a function of filler concentration together with the
required electrical conductivity values for different applications (95).
12
Fabrication of CNT/Polymer Composites
Figure 2.4. Electrical conductivity of single walled carbon nanotube/polystyrene composites
as a function of filler loading together with the required electrical conductivity values for
different applications (95).
2.4 Fabrication of CNT/Polymer Composites
Direct Mixing: Carbon nanotubes are dispersed into the thermosetting resins by mechanical
mixing or sonication. Then the resin is cured to obtain the CNT/polymer composite (13).
Melt Processing: This process is used when the insoluble polymers (in any solvent) are
considered. Polymers that melt upon heating (thermoplastic polymers) can be melted to form
liquids and nanotubes are added to this melt and mixed together. Achieving high
concentration and homogenous dispersion is difficult because of the high viscosities of the
mixtures. Shear mixing, extrusion and injection molding are some of the melt processing
methods (96).
In Situ Polymerization: Monomers are used as starting materials and are directly adhered to
the nanotube walls. It is mostly used for thermally unstable and insoluble polymers that
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Literature Survey
cannot be processed by melt processing (30). Park et al. (97) ultrasonicated the medium prior
to in situ polymerization to obtain well dispersed nanotubes.
Solution Method: Carbon nanotubes are added to the thermoplastic polymer-solvent
solution. The solvent is firstly used to dissolve the polymer but at the end of the process it
should be evaporated. Then the thermoplastic solidifies and composite is formed (98).
Agglomeration of the nanotubes during the solvent evaporation could be a potential problem
of this method (96).
2.5 Percolation Theory
Percolation theory is used to describe the disordered systems. For example transport in
composites can be explained by this theory. Consider a lattice, where a large array of squares
exists. Some of the squares are filled and the others are empty. We can assume that filled sites
are electrical conductors and empty sites are insulators. Then electrical current can flow only
between the neighboring electrical conductors (99). A cluster is defined as a group of
occupied neighbor squares.
At low concentrations, , most of the sites are insulators and conductors are isolated or form
small clusters which are not connected to the opposite edges. Therefore a current cannot flow
across the edges and we have zero conductivity. On the other hand, at large , the conductor
sites can form a conducting path between opposite edges and electrical current can flow. The
conductivity and the fraction of connected sites increase linearly with concentration. At some
point in between, a threshold concentration
should exist where the connected clusters
percolate for the first time through the lattice. This concentration is called the percolation
threshold (99) and represents the minimum volume fraction that a continuous conductive
network exists in the lattice (30).
Consider a section of bond cluster at percolation threshold. If a voltage is applied to the ends
of the cluster, some of the bonds will lead nowhere and they will not carry any current. These
bonds are called “dead ends” and will not contribute to the conductivity (Figure 2.5). When
these bonds are erased, “backbone” will be obtained and all the bonds of the backbone will
14